It looks like tags with two words, or tags with "space" characters are not correctly searched/displayed in the search result:

Replicated using:

• Moodle: 3.9.2+ (Build: 20201013)
• Database: MySQL 5.7.31
• Theme: Classic

Steps to replicate:

1. Create a course.
2. Turn editing on.
3. Add a Forum activity.
4. Go to the Forum activity.
5. Click "Add a new discussion topic" and click the "Advanced" link.
6. USe the values:
   • Subject: This is a new topic
   • Message: This is the content part.
7. Expand the Tags settings header.
8. On the "Enter tags textbox", type (and press enter):
   singleWordOnly
9. The tag should now be displayed as "x singleWordOnly"
10. Still on the "Enter tags textbox", type (and press enter): Two Words
11. The tag should now be saved and displayed as "x Two Words"
12. Click the "Post to forum" button.
13. After step 12, you will be redirected to the discussion list page.
14. Click on the "Search forums" button on the upper-right hand of the page.
15. Scroll down at the bottom of the page and in the "Is tagged with" section - Enter tags... textbox, type (and press enter): singleWordOnly
16. Click the "Search forums" button.
    Result: The results will be displayed. This is correct.
17. Go back to the Forum activity, click on the "Search forums" button again.
18. Scroll down at the bottom of the page and in the "Is tagged with" section - Enter tags... textbox, type (and press enter): Two Words
    Result: The page just refreshed, and displays "Search results No posts"

I have tested searching tags with "space" character as well here.

1. Go to: Navigation / Site pages / Tags
2. On the Search tags text box, type (and press enter): Two Words
   Result: Two Words link to the forum is displayed. Tags with "space" is searched/displayed correctly.